# Distributed Processing¶

This mode assumes that the data set is split into nblocks blocks across computation nodes.

## Algorithm Parameters¶

The correlation and variance-covariance matrices algorithm in the distributed processing mode has the following parameters:

Algorithm Parameters for Correlation and Variance-Covariance Matrices Algorithm (Distributed Processing)

Parameter

Default Valude

Description

computeStep

Not applicable

The parameter required to initialize the algorithm. Can be:

• step1Local - the first step, performed on local nodes

• step2Master - the second step, performed on a master node

algorithmFPType

float

The floating-point type that the algorithm uses for intermediate computations. Can be float or double.

method

defaultDense

Available methods for computation of low order moments:

defaultDense

default performance-oriented method

singlePassDense

implementation of the single-pass algorithm proposed by D.H.D. West

sumDense

implementation of the algorithm in the cases where the basic statistics associated with the numeric table are pre-computed sums; returns an error if pre-computed sums are not defined

fastCSR

performance-oriented method for CSR numeric tables

singlePassCSR

implementation of the single-pass algorithm proposed by D.H.D. West; optimized for CSR numeric tables

sumCSR

implementation of the algorithm in the cases where the basic statistics associated with the numeric table are pre-computed sums; optimized for CSR numeric tables; returns an error if pre-computed sums are not defined

outputMatrixType

covarianceMatrix

The type of the output matrix. Can be:

• covarianceMatrix - variance-covariance matrix

• correlationMatrix - correlation matrix

Computation of correlation and variance-covariance matrices follows the general schema described in Algorithms:

## Step 1 - on Local Nodes¶

In this step, the correlation and variance-covariance matrices algorithm accepts the input described below. Pass the Input ID as a parameter to the methods that provide input for your algorithm. For more details, see Algorithms.

Step 1: Algorithm Input for Correlation and Variance-Covariance Matrices Algorithm (Distributed Processing)

Input ID

Input

data

Pointer to the numeric table of size $$n_i \times p$$ that represents the $$i$$-th data block on the local node.

While the input for defaultDense, singlePassDense, or sumDense method can be an object of any class derived from NumericTable, the input for fastCSR, singlePassCSR, or sumCSR method can only be an object of the CSRNumericTable class.

In this step, the correlation and variance-covariance matrices algorithm calculates the results described below. Pass the Result ID as a parameter to the methods that access the results of your algorithm. For more details, see Algorithms.

Step 1: Algorithm Output for Correlation and Variance-Covariance Matrices Algorithm (Distributed Processing)

Result ID

Result

nObservations

Pointer to the $$1 \times 1$$ numeric table that contains the number of observations processed so far on the local node.

Note

By default, this result is an object of the HomogenNumericTable class, but you can define the result as an object of any class derived from NumericTable except CSRNumericTable.

crossProduct

Pointer to $$p \times p$$ numeric table with the cross-product matrix computed so far on the local node.

Note

By default, this table is an object of the HomogenNumericTable class, but you can define the result as an object of any class derived from NumericTable except PackedSymmetricMatrix, PackedTriangularMatrix, and CSRNumericTable.

sum

Pointer to $$1 \times p$$ numeric table with partial sums computed so far on the local node.

Note

By default, this table is an object of the HomogenNumericTable class, but you can define the result as an object of any class derived from NumericTable except PackedSymmetricMatrix, PackedTriangularMatrix, and CSRNumericTable.

## Step 2 - on Master Node¶

In this step, the correlation and variance-covariance matrices algorithm accepts the input described below. Pass the Input ID as a parameter to the methods that provide input for your algorithm. For more details, see Algorithms.

Step 2: Algorithm Input for Correlation and Variance-Covariance Matrices Algorithm (Distributed Processing)

Input ID

Input

partialResults

A collection that contains results computed in Step 1 on local nodes (nObservations, crossProduct, and sum).

Note

The collection can contain objects of any class derived from the NumericTable class except PackedSymmetricMatrix and PackedTriangularMatrix.

In this step, the correlation and variance-covariance matrices algorithm calculates the results described in the following table. Pass the Result ID as a parameter to the methods that access the results of your algorithm. For more details, see Algorithms.

Step 2: Algorithm Output for for Correlation and Variance-Covariance Matrices Algorithm (Distributed Processing)

Result ID

Result

covariance

Use when outputMatrixType=covarianceMatrix. Pointer to the numeric table with the $$p \times p$$ variance-covariance matrix.

Note

By default, this result is an object of the HomogenNumericTable class, but you can define the result as an object of any class derived from NumericTable except PackedTriangularMatrix and CSRNumericTable.

correlation

Use when outputMatrixType=correlationMatrix. Pointer to the numeric table with the $$p \times p$$ correlation matrix.

Note

By default, this result is an object of the HomogenNumericTable class, but you can define the result as an object of any class derived from NumericTable except PackedTriangularMatrix and CSRNumericTable.

mean

Pointer to the $$1 \times p$$ numeric table with means.

Note

By default, this result is an object of the HomogenNumericTable class, but you can define the result as an object of any class derived from NumericTable except PackedTriangularMatrix, PackedSymmetricMatrix, and CSRNumericTable.

Product and Performance Information

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex​.

Notice revision #20201201